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Full text of "Text Book Of Mechanical Engineering"

Efficiency of Carnot's Engine.

611

H being the effective work given to the engine.    Reckoning the
heat used, we have :

From i to 2 (r^). Heat expended, being work area i,

= P1V1 loge *i = ^ loge rv
From 2 to 3 (r%).   No heat expended, external work, j, being

done by abstraction of heat from the gas.
From 3 to 4 (r^). Heat rejected, as at K,

From 4 to i (r^).   No heat rejected, external work, at L, pro-
ducing internal work on the gas.

We have previously found (p. 607) the comparison of tempera-
ture in terms of r, during adiabatic expansion or compression :

from which may be deduced:

/Mv^
W

Referring to Fig. 617, expansion from 2 to 3 and compression
from 4 to i are between the same temperatures, so the ratio of
adiabatic expansion equals that of adiabatic compression : r2 = r±

And as, ~3 - ™4

V V

V2 V4

i      »»)             »q

and — = -
v,      v.

vl                   ,                                     vl

Or the ratio of isothermal expansion equals that of isothermal
compression: r^ = r^ = r, say.

Resuming; when the cycle is complete no internal work has
been done—all is external work:

. . External work = Heat expended - Heat rejected

=  CT   lOe   ^   - *r   lOge >     -  (T    ~ T     C

Efficiency of Engine :

Work done
Heat expended

--------17ET75-------"^   & &' 7<58' 883' 887'

i v.     &«   /         ------1—      934, and 966.)

It will be easily seen that for the highest efficiency, r2 must be
nothing, or the condenser must have a temperature of * absolute